Assessment Anchors Math Grade 7

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Math Grade 7Assessment Anchorsand Eligible Content

Pennsylvania Department of Education

www.pde.state.pa.us2007

http://www.pde.state.pa.us/

http://www.pde.state.pa.us/



Math, Grade 7

M7.A Numbers and Operations Reporting Category

Pennsylvania Department of Education Math Grade 7– Page 1

ASSESSMENT ANCHOR

M7.A.1 Demonstrate an understanding of numbers, ways of representing numbers,relationships among numbers and number systems.

ELIGIBLE CONTENT

M7.A.1.1 Express numbers in equivalent forms. M7.A.1.1.1 Convert between fractions, decimalsand/or percents (e.g., 20% = 0.2 =1/5) (terminating decimals only).

EXAMPLE ITEMS

• Note: This problem is solved without a calculator

Joshua buys a book that is on sale for5

1off.

What is the percent of discount for the price of the book?

A.201 %

B.5

1%

C. 5%D. 20%

(Maryland State Department of Education)*

Assessment Anchors and Eligible Content 2007



Math, Grade 7



ASSESSMENT ANCHOR

M7.A.1 Demonstrate an understanding of numbers, ways of representing numbers,relationships among numbers and number systems.

ELIGIBLE CONTENT

M7.A.1.2 Compare quantities and/or magnitudesof numbers.

M7.A.1.2.1 Compare and/or order integers,mixed numbers, fractions anddecimals (fractions and decimals maybe mixed – no more than 5 numbersin a set to be ordered).

M7.A.1.2.2 Locate/identify decimals, fractions,mixed numbers and/or integers on anumber line (a mix of these numberforms may be on the same numberline).

EXAMPLE ITEMS

•

Use the number line below to answer the question.

Which point on the number line is closest to17

22?

A. point PB. point QC. point RD. point S

(New Hampshire Department of Education)

• In which list of fractions are all of the fractions equivalent?

A.2

1,

4

2,

6

4

B.3

2,

6

4,

12

8

C.5

2,

10

4,

50

8

D.4

3,

6

4,

8

6

(TIMSS)

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Math, Grade 7



ASSESSMENT ANCHOR

M7.A.2 Understand the meanings of operations, use operations and understand how they relateto each other.

ELIGIBLE CONTENT

M7.A.2.1 Complete calculations by applying theorder of operations.

M7.A.2.1.1 Use the order of operations to simplifynumerical expressions (may useparentheses, brackets, +, -, x, ÷,squares up to 10

2and cubes up to 4

3;

whole numbers only).

EXAMPLE ITEMS

• Which of the following is a true sentence?

A. 2 + (3 x 5) – 4 = 13B. (2 + 3) x 5 – 4 = 13C. (2 + 3) x (5 – 4) = 13

D. none of the above (New Hampshire Department of Education)

• Look at the expression below.12 + 4 x (12 – 9)

What is the value of the expression?

A. 24B. 48C. 51D. 55

(Maryland State Department of Education)

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Math, Grade 7



ASSESSMENT ANCHOR

M7.A.2 Understand the meanings of operations, use operations and understand how they relateto each other.

ELIGIBLE CONTENT

M7.A.2.2 Solve problems using ratios,proportions, percents and/or rates.

M7.A.2.2.1 Write ratios to compare quantities(e.g., ratio of boys to girls).

M7.A.2.2.2 Solve for a variable in a givenproportion.

M7.A.2.2.3 Use proportions to determine if twoquantities are equivalent (e.g., similarfigures, prices of different sized items,etc).

M7.A.2.2.4 Calculate and/or apply unit rates orunit prices (terminating decimals

through the hundredth place only).

M7.A.2.2.5 Select and/or use ratios orproportions to solve problems.

M7.A.2.2.6 Use proportions to find the missinglength of a side in similar figures.

EXAMPLE ITEMS




Math, Grade 7



ASSESSMENT ANCHOR

M7.A.3 Compute accurately and fluently and make reasonable estimates.

ELIGIBLE CONTENT

M7.A.3.1 Apply estimation strategies to a variety

of problems.

M7.A.3.1.1 Estimate answers to problems

involving whole numbers, decimals,fractions or mixed numbers.

EXAMPLE ITEMS

• Use the picture below to answer the question.

The Anderson family consists of two adults and two children, Brian, age 5, and Andrea, age 3.Which is the closest estimate of what it will cost the family to ride on the Scenic Railroad?

A. $30.00B. $20.00C. $15.00D. $10.00


*




Math, Grade 7



ASSESSMENT ANCHOR

M7.A.3 Compute accurately and fluently and make reasonable estimates.

ELIGIBLE CONTENT

M7.A.3.2 Compute accurately with and without

use of a calculator.

M7.A.3.2.1 Solve problems involving operations

(+, -, x, ÷) of whole numbers,decimals, fractions, or mixed numbers(straight computation or wordproblems)

M7.A.3.2.2 Solve problems involving addition andsubtraction of integers.

EXAMPLE ITEMS




Math, Grade 7

M7.B Measurement Reporting Category


ASSESSMENT ANCHOR

M7.B.1 Demonstrate an understanding of measurable attributes of objects and figures, and theunits, systems and processes of measurement.

ELIGIBLE CONTENT

M7.B.1.1 Add, subtract, or convertmeasurements.

M7.B.1.1.1 Add, subtract, or convertmeasurements, using only the unitsbelow, with and without regrouping(e.g., 4ft – 2ft 5in = 1ft 7in). Answershould be converted to the largestwhole unit (e.g., 37oz = 2 Lb 5oz or39 in = 1 yd 3 in. Conversion chartprovided on the reference sheet.• in, ft, yd• fl oz, cup, pint, quart, gallon• oz, Lb• sec, min, hours, days• metric units including milli, centi

and kilo (m, g or L)

EXAMPLE ITEMS

• At the state track meet, Steve averaged 1 minute, 28 seconds, per lap. How long did it takehim to finish the four-lap race?

A. 5 minutes, 12 secondsB. 5.12 minutesC. 5 minutes, 52 secondsD. 5.52 minutes


*




Math, Grade 7



ASSESSMENT ANCHOR

M7.B.2 Apply appropriate techniques, tools and formulas to determine measurements.

ELIGIBLE CONTENT

M7.B.2.1 Develop, use and/or describe strategies

to find the measure of length, perimeter,circumference, area or volume.

M7.B.2.1.1 Develop and/or use strategies to find

the perimeter and/or area ofcompound figures (compound figuresshould only include quadrilaterals andtriangles). Area formulas provided onthe reference sheet.

M7.B.2.1.2 Find the circumference and/or area ofcircles (formulas provided on thereference sheet).

M7.B.2.1.3 Find the area of triangles and/or alltypes of parallelograms (formulasprovided on the reference sheet).

EXAMPLE ITEMS

• The square chessboard shown below has an area of 144square inches.

Note: The figure is not drawn to scale.

What is the length, in inches, of one side of the chessboard?

A. 6 inchesB. 12 inchesC. 36 inchesD. 72 inches

(Maryland State Department of Education)

*




Math, Grade 7



ASSESSMENT ANCHOR

M7.B.2 Apply appropriate techniques, tools and formulas to determine measurements.

ELIGIBLE CONTENT

M7.B.2.2 Construct, interpret and/or use scale

drawings to solve real-world problems.M7.B.2.2.1 Interpret and/or apply scales shown

on maps, blueprints, models, etc.

M7.B.2.2.2 Determine and/or apply anappropriate scale for reduction orenlargement.

EXAMPLE ITEMS




Math, Grade 7

M7.C Geometry Reporting Category


ASSESSMENT ANCHOR

M7.C.1 Analyze characteristics and properties of two- and three- dimensional geometric shapesand demonstrate understanding of geometric relationships.

ELIGIBLE CONTENT

M7.C.1.1 Define and/or apply basic properties oftwo- and three-dimensional geometricshapes.

M7.C.1.1.1 Identify, describe and/or definediameter, radius, chord and/orcircumference in circles.

M7.C.1.1.2 Solve problems involving therelationship between the radius anddiameter of the same circle.

M7.C.1.1.3 Identify parallel, perpendicular and/orskew line segments within three-dimensional figures.

EXAMPLE ITEMS






Math, Grade 7



ASSESSMENT ANCHOR

M7.C.2 Identify and/or apply concepts of transformations or symmetry.

ELIGIBLE CONTENT

Not assessed at Grade 7.

EXAMPLE ITEMS




Math, Grade 7



ASSESSMENT ANCHOR

M7.C.3 Locate points or describe relationships using the coordinate plane.

ELIGIBLE CONTENT

M7.C.3.1 Locate, plot and/or describe points on a

coordinate plane.

M7.C.3.1.1 Plot and/or identify ordered pairs on a

coordinate plane (all four quadrants).

M7.C.3.1.2 Identify Quadrants I, II, III, IV, the x- &y-axes and the origin on a coordinateplane.

EXAMPLE ITEMS




Math, Grade 7

M7.D Algebraic Concepts Reporting Category

ASSESSMENT ANCHOR

M7.D.1 Demonstrate an understanding of patterns, relations and functions.

ELIGIBLE CONTENT

M7.D.1.1 Recognize, reproduce, extend and/or

describe patterns.

M7.D.1.1.1 Describe, extend or find a missing

element of a pattern (show 3repetitions of the pattern)• fractions or decimals - may use

only one operation from +, - or x• whole numbers – may use only

one operation from +, -, x, ÷ orsquares

EXAMPLE ITEMS

• Use the pattern below to answer the question.

What is the next figure in this pattern?


A.*B.

C.

D.





Math, Grade 7


ASSESSMENT ANCHOR

M7.D.2 Represent and/or analyze mathematical situations using numbers, symbols, words,tables and/or graphs.

ELIGIBLE CONTENT

M7.D.2.1 Select and/or use appropriate strategiesto solve or represent equations orexpressions.

M7.D.2.1.1 Select and/or use appropriatestrategies to solve one-step equations(no negative numbers).

M7.D.2.1.2 Use substitution of one and/or twovariables to simplify expressions(whole numbers only – use order ofoperations).

EXAMPLE ITEMS

• Given the replacement set {11, 13, 105, 109}, what must n be to make the sentence true?

3 x n – 2 = 37

A. 11B. 13C. 105D. 109


*





Math, Grade 7


ASSESSMENT ANCHOR

M7.D.2 Represent and/or analyze mathematical situations using numbers, symbols, words,tables and/or graphs.

ELIGIBLE CONTENT

M7.D.2.2 Create and/or interpret expressions,equations or inequalities that modelproblem situations.

M7.D.2.2.1 Identify expressions, equations orinequalities that model mathematicalsituations (using whole numbers ordecimals, no more than two operationsand one variable).

EXAMPLE ITEMS





Math, Grade 7


ASSESSMENT ANCHOR

M7.D.3 Analyze change in various contexts.

ELIGIBLE CONTENT

M7.D.3.1 Describe the relationship between two

variables (e.g., time, temperature). M7.D.3.1.1 Solve problems involving a constant

rate of change (e.g., word problems,graphs or data tables).

M7.D.3.1.2 Describe and/or use the relationship ofdata displayed on a rate of changegraph (e.g., how does the x-axis datarelate to the y-axis data).

EXAMPLE ITEMS

• Daniel drove 480 km in 4 hours. If Daniel continues driving at the same speed, how long will it takehim to drive an additional 720 km?

A. 18 hoursB. 12 hours

C. 6 hours

D. 3 hours

(Pennsylvania Department of Education)

•

It takes Jan 10 minutes to skate downtown from school. Skating at the same speed, it takesabout 38 minutes to skate home from downtown. About how far from downtown does Jan live?

A. 2 miles

B. 4 miles

C. 8 miles

D. 13 miles

*

*(New Hampshire Department of Education)





Math, Grade 7


ASSESSMENT ANCHOR

M7.D.4 Describe or use models to represent quantitative relationships.

ELIGIBLE CONTENT

Not assessed at Grade 7.

EXAMPLE ITEMS





Math, Grade 7

M7.E Data Analysis and Probability Reporting Category

ASSESSMENT ANCHOR

M7.E.1 Formulate or answer questions that can be addressed with data and/or organize, display,interpret or analyze data.

ELIGIBLE CONTENT

M7.E.1.1 Interpret data shown in complex datadisplays.

M7.E.1.1.1 Analyze data and/or answer questionspertaining to data represented inhistograms, double bar graphs,multiple line graphs or stem-and-leafplots.

EXAMPLE ITEMS

• Use the graph below to answer the question.

According to this graph, during which 20-yearperiod did the colonial population of NewHampshire grow fastest?

A. 1700 – 1720B. 1670 – 1690C. 1650 – 1670D. 1630 – 1650


*





Math, Grade 7


ASSESSMENT ANCHOR

M7.E.2 Select and/or use appropriate statistical methods to analyze data.

ELIGIBLE CONTENT

M7.E.2.1 Describe, compare and/or contrast data

using measures of mean, median, modeor range.

M7.E.2.1.1 Identify/calculate the mean (average),

median, mode or range of a set ofdata.

M7.E.2.1.2 Decide/choose which measure ofcentral tendency (mean, median,mode or range) would be mostappropriate for a given situation.

EXAMPLE ITEMS

• The salaries of the employees at Dean’s Print Shop are $24,000, $37,000, $12,000, $17,000,$26,000, $40,000 and $19,000.

What is the median salary of the employees

A. $25,000B. $24,000C. $17,000D. $12,000

(New Jersey Department of Education)

• Tetsu rides his bicycle x miles for the first day, y miles the second day, and z miles the thirdday. Which of the following expressions represents the average number of miles per day thatTetsu travels?

A. x + y +zB. xyz

C. 3(x + y + z)D. 3(xyz)E. (x + y + z)/3

(NAEP)

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*• The table shows the number of gallons of paint sold at a paint store each week in one month.

WeekAverage Numberof Gallons Sold

1 2352 4123 3574 286

What was the MEAN number of gallons of paint sold each week at this store?

A. 321.5B. 177C. 260.5D. 322.5

(Connecticut Department of Education)





Math, Grade 7


ASSESSMENT ANCHOR

M7.E.3 Understand and/or apply basic concepts of probability or outcomes.

ELIGIBLE CONTENT

M7.E.3.1 Determine theoretical or experimental

probability.

M7.E.3.1.1 Find the theoretical probability of a

simple and/or compound event(answer written as a fraction in lowestterms – any compound events shouldbe independent)

M7.E.3.1.2 Find the theoretical probability of anevent not occurring (e.g., what is theprobability of not rolling a 1 on anumber cube)

M7.E.3.1.3 Use data displayed in charts, graphsor tallies to find experimentalprobability

EXAMPLE ITEMS





Math, Grade 7


ASSESSMENT ANCHOR

M7.E.4 Develop and/or evaluate inferences and predictions or draw conclusions based on dataor data displays.

ELIGIBLE CONTENT

M7.E.4.1 Draw conclusions and/or makepredictions based on data displays.

M7.E.4.1.1 Formulate predictions and/or drawconclusions based on data displays(bar graphs, circle graphs or linegraphs) or probability.

EXAMPLE ITEMS

• This table lists the average temperatures recorded on Mt. Washington over a 30-year period.Based on the table, what is the most likely average temperature on Mt. Washington in October?

Month Temperature (°C)Jan. -15Mar. -10May 1

Jul. 9Sep. 4Nov. -6

A. –5°CB. –1°CC. 1°CD. 5°C


• Use the graph below to answer the question.

According to the graph, how much would four bags of popcorn cost?

A. $4.00B. $4.25C. $4.50D. $5.00


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Assessment Anchors Math Grade 7